Superposed Hyperbolic Kink and Pulse Solutions of Coupled $ϕ^4$, NLS and MKdV Equations

Abstract

We obtain novel solutions of a coupled φ 4 , a coupled nonlinear Schrödinger (NLS) and a coupled modified Korteweg de Vries (MKdV) model which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic kink or two hyperbolic pulse solutions. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well.

Superposed periodic kink and pulse solutions of coupled nonlinear equations

“…In another publication, we further extended the notion of the superposition principle for coupled nonlinear equations. In particular, we showed that the coupled φ 4 , coupled NLS, and coupled mKdV equations admit novel solutions which can be re-expressed as the superposition of a (hyperbolic) kink and an antikink or two (hyperbolic) kinks or two (hyperbolic) pulse solutions [16].…”

“…The purpose of this paper is to answer this question in the affirmative. In particular, we consider the same coupled φ 4 model and the coupled NLS model discussed in [16] and show that both these models admit novel periodic solutions which can be re-expressed as either the sum of a periodic kink and an antikink or two periodic kinks or two periodic pulse solutions.…”

“…In Sec. III, we discuss the coupled nonlinear Schrödinger equation (NLS) model as discussed in [16] and show that it also admits novel solutions which can be re-expressed as superposition of either a periodic kink and an antikink, or two periodic kinks or two periodic pulse solutions. Finally, in Sec.…”